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分析学中的一类反例函数

发表时间:2010-01-15  浏览量:1954  下载量:869
全部作者: 顾先明,侯海山,朱守强,宋泽成
作者单位: 唐山师范学院数学与信息科学系
摘 要: 为加强高等学校分析学课程的教学效果,帮助学生深刻理解和抓住概念及定理的实质内容,采用大量列举实例对分析学中的常见反例问题进行较为深入的研究,并对相关的参考文献提出修改意见,给出一种应用广泛的反例形式。研究了一类函数在分析学相关反例构造中的应用,进一步指出有关函数的连续、可导、可积等分析性质的概念与定理中容易出现的误区,并给出相应的反例,希望能引起高校师生对该类函数的重视,进一步提高教学效果。
关 键 词: 数学分析;反例构造;连续;广义导数;可积
Title: A kind of counterexample function in the analysis
Author: GU Xianming, HOU Haishan, ZHU Shouqiang, SONG Zecheng
Organization: Department of Mathematics and Information Science, Tangshan Teacher’s College
Abstract: In order to strengthen the teaching effect of higher learning analytics courses and help students understand and grasp the profound substance of the concepts and theorems, the paper featured a host of examples to do a more in-depth study of the common counter-examples issue in the analytics, and gave modification suggestions for the relevant reference and a widely used form of counter-examples. The paper studied how to structure a kind of counterexample function in the analysis and widespread application emphatically, further pointed out the misunderstandings easily appeared in the concept and theorem of continuity, derivable, integrable, and other analytic properties of the function and gave the corresponding counter-example finally.
Key words: mathematical analysis; counterexample structure; continuity; generalized derivatives; integrable
发表期数: 2010年1月第1期
引用格式: 顾先明,侯海山,朱守强,等. 分析学中的一类反例函数[J]. 中国科技论文在线精品论文,2010,3(1):61-69.
 
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